The measure of the third angle in the triangular sail, given that the largest angle is 90° and the smallest angle is x°, is found by subtracting the known angles from 180°, giving the expression 90° - x°.
Explanation:In a triangular sail, the sum of all the angles totals to 180°. Given that the largest angle measures 90° and the smallest angle measures x°. We find the measure of the third angle by using the fact that the sum of angles in a triangle equals 180 degrees. Therefore, if we subtract the two known angles from 180, we can locate the measure of the third angle. So the expression to determine the third angle in degrees would be 180° - 90° - x°, simplifying the expression to 90° - x°.
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Factor the expression completely over the complex numbers. x4+10x2+25
Answer:
[tex](x-i\sqrt 5)^2(x+i\sqrt5)^2[/tex]
Step-by-step explanation:
We are given that an expression
[tex]x^4+10x^2+25[/tex]
We have to find the factorize the expression completely over the cmplex number.
[tex](x^2+5)^2[/tex]
Using identity [tex](a+b)^2=a^2+b^2+2ab[/tex]
[tex](x^2+5)(x^2+5)[/tex]
Substitute each factor equal to zero.
[tex]x^2+5=0[/tex] ,[tex]x^2+5=0[/tex]
[tex]x^2=-5[/tex]
[tex]x=\pm \sqrt{-5}=\pm i \sqrt 5[/tex]
[tex]x=i\sqrt 5[/tex] and [tex]x=-i\sqrt 5[/tex]
[tex]x-i\sqrt 5=0[/tex] and [tex]x+i\sqrt 5=0[/tex]
The factor of second term is also same
Therefore, the factors of the expression completely is given by
[tex](x-i\sqrt 5)^2(x+i\sqrt5)^2[/tex]
The solution to the quadratic equation is ±5i
Factorizing quadratic equationsGiven the expression below:
x^4+10x^2+25 = 0
Let P = x^2
Substituting into the expression, we will have;
P^2 + 10P + 25 = 0
Factorizing the expression, we will have:
P^2 + 10P + 25 = 0
P^2 + 5P+ 5P + 25 = 0
P(P+5) + 5(P + 5) = 0
(P+5)(P+5) = 0
P = - 5 twice
Substitute into the given substitute
x^2 = -5
x = √-5
x = ±5i
Hence the solution to the quadratic equation is ±5i
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A movie theater has 250seats. 3250 tickets were sold at the theater. How many movies were shown at the theater last week if every person who bought a ticket saw a movie and every seat was filled for each feature?
answer will be equal to 3250 divided by 250 which is 13
The metric system is based on the number ___. 1 2 10 12
Answer:
The metric system is based on the number 10.
Step-by-step explanation:
We have been given an incomplete statement. We are asked to fill in the blank for given statement.
The metric system is based on the number ___.
We know that metric system is an alternative system of measurement used in most countries including the United States. This system includes prefixes like kilo-, hecto-, deka-, deci-, centi-, and milli.
The metric system is based on number 10 as all these units are based on power of 10.
Therefore, option C is the correct choice.
The metric system is based on the number 10.
Here, we have,
The metric system is a decimal-based system of measurement that is widely used around the world. It is designed to be a coherent and consistent system, with units of measurement that are related to each other by powers of 10.
In the metric system, there is a base unit for each quantity being measured, such as meters for length, grams for mass, and liters for volume. The prefixes are then used to indicate multiples or fractions of the base unit. These prefixes are based on powers of 10, which allows for easy conversions between different units within the system.
For example, when we go from a larger unit to a smaller unit within the same measurement category, we move the decimal point to the right by powers of 10. Likewise, when we go from a smaller unit to a larger unit, we move the decimal point to the left by powers of 10.
This decimal-based nature of the metric system makes it highly convenient for scientific and everyday use, as it simplifies calculations and conversions.
The metric system is based on number 10 as all these units are based on power of 10.
Therefore, option C is the correct choice.
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SOMEONE PLZ HELP
Write the recursive rule of the sequence -9, -3, 3, 9,... .
________________________________________
-A line has an x-intercept of (4, 0) and a y-intercept of (0, 12). Find the slope of the line.
________________________________________
-A horizontal line includes the points (0, -5 ) and ( 2, -5 ) Find the slope of the line.
1.Suppose f(x)=6x^2+2x-7 and g(x)=4x-3.Find Each Of The Following Function.
a. (f+g)(x)
b.(f-g)(x)
2.Suppose f(x)=2x-3x and g(x)=1-2x. Find Each Of The Following Functions.
a. (f+g)(x)
b.(f-g)(x)
(1)
(f+g)(x) = 6x^2+2x-7+4x-3=6x^2+6x-10
(f-g)(x)=6x^2+2x-7-4x+3 = 6x^2-2x-4
(2)
(f+g)(x)=2x-3x+1-2x=-3x+1
(f-g)(x)=2x-3x-1+2x=x-1
Can someone please help me?
The graph shows a journey in a car. Which of the statements most likely describes the start of the journey at the portion of the graph labeled I?
When evaluating a complex expression which of the following rules should be followed
A - Evaluate from left to right
B - Evaluate from right to left
C- Evaluate using order of operations
D- Evaluate in any order
c : evaluate using order of operations ( pemdas )
Option: C is the correct answer.
C- Evaluate using order of operations
Step-by-step explanation:We know that while solving a algebraic expression we must follow the rule:
PEMDAS
whose full form is:
Parenthesis , Exponents,Multiplication division addition and subtraction.
This means that parenthesis is to be solved first then the preference is given to the exponent, then division and multiplication are treated at the same level and the last preferred operation is addition and subtraction.
Hence, the correct answer is:
Option: C
Simplify m - {n - [p + (m + n - p)]}.
0
2m
-2m + 2p
2.Select the correct difference.
-3z 5 - (-7z 5)
Answer:
0
4z^5
Step-by-step explanation:
We are asked to
Simplify m - {n - [p + (m + n - p)]}.
For that we remove first internal bracket and then next in the same order.
= m - {n - [p + m + n - p]}. (by removing the inner bracket)
Now we simplify the term inside by cancelling p
= m - {n - [ m + n ]}. Next is multiply by - the term m+n.
= m-[n-m-n]. Now n cancels out.
=m-(m) = 0
Finally we get 0 as answer.
0
2m
-2m + 2p
2.Select the correct difference.
-3z^ 5 - (-7z^ 5)
= 3z^5+7z^5
= 4z^5
Find the product of (3x+7y)^2
A) 9x^2 - 42xy + 49y^2
B) 9x^2 - 49y^2
C) 9x^2 + 49y^2
D) 9x^2+42xy+49y^2
Answer:
9x^2 − 42xy + 49y^2
Step-by-step explanation:
The product of [tex](3x + 7y)^2[/tex] is: D)[tex]9x^2 + 42xy + 49y^2[/tex]
How to find the productsThe product of (3x + 7y)^2 can be found using the formula for squaring a binomial:
(3x + 7y)^2 = (3x + 7y)(3x + 7y)
To calculate this product, you can use the distributive property (FOIL method):
(3x + 7y)(3x + 7y) = (3x * 3x) + (3x * 7y) + (7y * 3x) + (7y * 7y)
Now, simplify each term:
(9x^2) + (21xy) + (21xy) + (49y^2)
Combine like terms:
9x^2 + 42xy + 49y^2
So, the product of [tex](3x + 7y)^2[/tex] is:
D)[tex]9x^2 + 42xy + 49y^2[/tex]
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Sam took out an 80/20 mortgage on a $205,000 home. What is the amount financed under the first mortgage
a.$164,000
b.$41,000
c.$205,000
d$120,000
Given condition is: Sam took out an 80/20 mortgage on a $205,000 home.
Here, 80/20 refers to 80% mortgage amount means it will be paid as mortgage and 20% loan amount.
So, to find the amount financed under the first mortgage, we will find 80% of 205000.
[tex]\frac{80}{100}\times205000[/tex]
= $164000
Hence, option A is the correct answer.
PLEASE HELP ASAP
The length of a rectangle is 6m longer than its width. What are the possible widths if the area of the rectangle is at least 775cm^2?
Hey there!!
What is the area of a rectangle?
The area of a rectangle = Length × Breadth
Given :
Length is 6m longer than the width.
Hence, length = 6 + breadth
Area = ( 6 + breadth ) ( breadth )
Area = 6 breadth + breadth²
Area = 775
Hence, 775 = 6 breadth + breadth²
( Let's take the breadth as ' b ' )
775 = 6b + b²
... b² + 6b - 775 = 0
... b² - 25b + 31b - 775 = 0
... b ( b - 25 ) + 31 ( b - 25 ) = 0
... ( b + 31 ) ( b -25 ) = 0
There are two solutions found :
b + 31 = 0 and b - 25 = 0
Hence,
b = -31 and b = 25
As the values can not be in negatives, we take 25
Hence, the value of the breadth is 25.
Length = 6 + b
Length = 31
Hence, the value of the length = 31
Hope my answer helps!!
write an equation of a parabola with vertex at origin (0,0) with the given focus, and find the directrix. given the focus at (0,-4)
Directrix:
If the vertex of the parabola is at (0, 0) and the focus is (0, -4) which is 4 units down then the directrix will be the line 4 units UP.
Answer: y = 4
Equation of parabola:
[tex]y = \frac{1}{4p}x^{2}[/tex] ; where p is the distance from the vertex to the focus.
As stated above, the focus is 4 units down, so p = -4
[tex]y = \frac{1}{4(-4)}x^{2}[/tex]
[tex]y = \frac{1}{-16}x^{2}[/tex]
Answer: [tex]y = -\frac{1}{16}x^{2}[/tex]
Does 14.2857143 rounded to a whole number
Multiply. (7x-4)(4x-3)
Your answer is 28x^2-37x+12
1) Use the FOIL method: (a+b)(c+d)=ac+ad+bc+bd
28x^2-21x-16x+12
2) Collect like terms
28x^2+(-21-16x)+12
3) Simplify
28x^2-37x+12
Use FOIL
28x-21x-16x+12
-9x+12
Please help with geometry homework!!!!
Area of Parallelogram ABCD is equivalent to the area of rectangle AXBY.
Area of rectangle AXBY= Length AX * Length AB= 3 ft * 4√2 ft = 12√2 sq.ft.
Thus Area of Parallelogram is 12√2 sq.ft.
Which of the following is the correct expansion of (x - 2)(x - 5)?
x2 + 7x + 10
x2 + 7x - 10
x2 - 7x - 10
x2 - 7x + 10
Use distributive property:
(a + b)(c + d) = ac + ad + bc + bd
(x - 2)(x - 5) = (x)(x) + (x)(-5) + (-2)(x) + (-2)(-5) = x² - 5x - 2x + 10
Answer: (x - 2)(x - 5) = x² - 7x + 10find the quotient and remainder. Please select the vest abswer from the answer choices
Answer:
Quotient = x^4 + x^3 + x^2 + x + 1
Remainder = 0
Step-by-step explanation:
(x^5 +1) is divided by (x - 1) as shown below:
(x^5 +1) / (x - 1)
where x^5 is divided by (x - 1) when multiplied by x^4 (quotient) to give x^4 - 1.
Now x^4 - 1 is divided by is divided by (x - 1) when multiplied by x^3 (quotient) to give x^3 - 1.
Then again x^3 - 1 is divided by (x - 1) when multiplied with x^2 (quotient) to give x^2 -1.
x^2 - 1 is divided by (x - 1) when multiplied by x to give (x - 1).
Lastly, (x - 1) is divided by (x - 1) when multiplied by 1 to cancel the terms with remainder 0.
in a class of 30 students. 13 of them are boys.
what percentage of the class are girls?
give your answer to 1 decimal place.
Hello...
Students - 30
Boys - 13
Girls - ?
30 - 13 = 17
There are 17 girls!
Percentage:
17 / 30 = 0.56666666667...
= 56.6...
Answer:
56% are girls
44% are boys
56.66% is the percentage of the class are girls.
What is Percent?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is primarily used to compare and determine ratios and is represented by the symbol %.
Given:
Total students= 30
Number of boys= 13
Number of girls = 30- 13 = 17
So, percentage of the class are girls
= 17 /30 x 100
= 0.56666x 100
= 56.66%
Hence, 56.66% is the percentage of the class are girls.
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The product of two numbers is 40. If one of the numbers is 8/15, what is the other number?
When the product of two numbers is 40 and one of the numbers is 8/15, the other number can be found by dividing 40 by 8/15, which is 937.5.
Explanation:The question is asking for the other number when the product of two numbers is 40 and one of the numbers is given as 8/15. To answer this, we need to use the concept that the product of two numbers is equal to one number multiplied by the other. Therefore, to find the missing number, we need to divide 40 (the product) by the given number (8/15).
So, the calculation will look like this: 40 ÷ (8/15) = 7500/8 = 937.5.
Thus, the other number is 937.5 .
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Jim has answered 7 e-mails this is 35% of the e-mails he must answer how many emails does he need to answer?
Answer: He needs to answer 20 emails.
Step-by-step explanation:
Given : Jim has answered 7 e-mails . (1)
This is 35% of the e-mails he must answer .
We can write 35% as 0.35.
Let x be the number of emails he need to answer.
Then, Number of mails he has answered = 0.35x (2)
From (1) and (2), we have
[tex]0.35=7\\\\\Rightarrow\ x=\dfrac{7}{0.35}=\dfrac{700}{35}=20[/tex]
Hence, he needs to answer 20 emails.
please please please help!
Answer:
it is a neg slope
Step-by-step explanation:
PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!
Solve.
x^2 − 9x + 3 = 0
At a restaurant, the bill comes to $60. If you decide to leave a 14% tip, how much is the tip?
60 times 0.14 = 8.4
You would give $8.40 as a tip of 14% from a bill of $60
Final answer:
To calculate a 14% tip on a $60 bill, you multiply 0.14 by $60, resulting in a tip of $8.40.
Explanation:
To find out how much a 14% tip is on a $60 bill, we need to convert the percentage into a decimal by dividing by 100.
This gives us 0.14 as the decimal form of 14%.
We then multiply this decimal by the total bill amount to calculate the tip: 0.14 × $60 = $8.40
Therefore, the tip would be $8.40.
Write the following statement as a conditional statement.
Stars have ten vertices.
A) If a figure has ten vertices, then it is a star.
B) A figure is a star, if and only if, it has ten vertices.
C) Star are figures with ten vertices.
D) If a figure is a star, then it has ten vertices.
A) If a figure has ten vertices, then it is a star. This is the correct conditional statement.
Conditional statement can be simplified as : if a, then b. Here 'a' is one condition and 'b' is second condition. So, based on this, option A is correct.
Answer:
The correct option is D.
Step-by-step explanation:
The given statement is "Stars have ten vertices".
If a complete statement has two sub statements p and q, then the conditional statement is "If p, then q", where p is a hypothesis and q is a conclusion.
In the given statement,
p = A figure is a star.
q = It has ten vertices
So, the conditional statement of the given statement is
If a figure is a star, then it has ten vertices.
Therefore the correct option is D.
Complete the two column proof
a. is Substitution Property
b. might be definition of supplementary angles
Answer:
B is the sum of adjacent angles is 180 degrees
Step-by-step explanation:
It is showing you that m∠3 and m∠4 "=" 180
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Marty ran 4 miles more than Shana ran. Write an expression for how far Shana ran using Marty’s variable “m”
Explain what the 4 inequality signs represent in your own words
The expression would be m - 4 because if Marty ran 4 more miles than Shana, that means that Shana ran 4 less miles than Marty.
The four inequalities are less than, less than or equal to, greater than, and greater than or equal to. Less than means that a number is less than the other number. For example, if you say 4 is less than 7 it is because 4 is less than 7 by 3 which makes 7 value more than 4. For less than or equal to, it means that the number or variable is less than or the same number as the other number. For example, if you say x is less than or equal to 9, that means that x is less than 9 or equal to 9. For greater than, it means that the variable is greater than the other number. For example, if x if greater than 10 than the variable has to be greater than 10 or 11 and so on. For greater than or equal to, it means that the variable is greater than the other number or equal to that number. For example, if x is greater than or equal to 12, then x is greater than 12 or 13 and up or x is equal to 12 or x is 12.
please help on this one?
I think it is B. If you drew a graph of this and the x axis was time and the y axis is the enrollment then you would get 3 different x values and 1 y value. That's still a function. I've drawn it below.
Her goal was to rased 5000 dollers to help protect the manites she rased 3500 what persent of the goal did she rase
Animal shelter house ratio catch a dog that is 9:7. If the shelter only as his dogs and cats what is the ratio of dogs total animals?
Answer:
The ratio of dogs to animals [tex]\frac{9}{16}[/tex].
Step-by-step explanation:
If the shelter captures 9 dogs they also catch 7 cats.
So,
the total number of Animals = Total number of Dogs + Total number of Cats
= [tex]9+7[/tex]
=[tex]16[/tex]
Therefore,
The ratio of dogs to animals = Number of Dogs / Total number of animals
= [tex]\frac{9}{16}[/tex]
7/16
7 is dog 9 is cat
7+9=16
Solve the system equation.
Answer:
A) (0, 2)
Step-by-step explanation:
Rewriting the second equation to the same form as the first, it becomes
... 1/2y = x + 1
... y = 2x + 2
Now, it is clear that both equations have the same y-intercept at y=2, so that is the solution.
... (x, y) = (0, 2)